RGPV TOC properties of transition functions

Q. State and explain the properties of transition functions ?

Ans. A transition function is defined on every state for every input symbol.
Transition Function (δ) is defined as δ = Q X Σ –> Q.

Q is set of all states.
Σ is set of input symbols.
Properties of transition functions:
Property 1: δ(q,Λ) = q. It means the state of a system can be changed by an input symbol.
Property 2: For all strings w and input symbol a,
δ(q, aw) = δ(δ(q,a),w) 
δ(q, wa) = δ(δ(q,w), a)
It means the state after the automaton consumes or reads the first symbol of a string aw and the state after the automaton consumes a prefix of the string wa.